Electronic Journal of Statistics

Improved classification rates under refined margin conditions

Ingrid Blaschzyk and Ingo Steinwart

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In this paper we present a simple partitioning based technique to refine the statistical analysis of classification algorithms. The core of our idea is to divide the input space into two parts such that the first part contains a suitable vicinity around the decision boundary, while the second part is sufficiently far away from the decision boundary. Using a set of margin conditions we are then able to control the classification error on both parts separately. By balancing out these two error terms we obtain a refined error analysis in a final step. We apply this general idea to the histogram rule and show that even for this simple method we obtain, under certain assumptions, better rates than the ones known for support vector machines, for certain plug-in classifiers, and for a recently analyzed tree based adaptive-partitioning ansatz. Moreover, we show that a margin condition which sets the critical noise in relation to the decision boundary makes it possible to improve the optimal rates proven for distributions without this margin condition.

Article information

Electron. J. Statist., Volume 12, Number 1 (2018), 793-823.

Received: October 2016
First available in Project Euclid: 3 March 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62H30: Classification and discrimination; cluster analysis [See also 68T10, 91C20]
Secondary: 62G20: Asymptotic properties 68T05: Learning and adaptive systems [See also 68Q32, 91E40]

Statistical learning classification excess risk fast rates of convergence histogram rule

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Blaschzyk, Ingrid; Steinwart, Ingo. Improved classification rates under refined margin conditions. Electron. J. Statist. 12 (2018), no. 1, 793--823. doi:10.1214/18-EJS1406. https://projecteuclid.org/euclid.ejs/1520046229

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